Solve 3/7+[-6/11]+[-8/19]+5/29

$$\frac { 3 } { 7 } + [ \frac { - 6 } { 11 } ] + [ - \frac { 8 } { 19 } ] + \frac { 5 } { 29 }$$

Evaluate

$$-\frac{15508}{42427}\approx -0.365521955$$

Solution Steps

Fraction \frac{-6}{11} can be rewritten as -\frac{6}{11} by extracting the negative sign.

$$\frac{3}{7}-\frac{6}{11}-\frac{8}{19}+\frac{5}{29}$$

Least common multiple of 7 and 11 is 77. Convert \frac{3}{7} and \frac{6}{11} to fractions with denominator 77.

$$\frac{33}{77}-\frac{42}{77}-\frac{8}{19}+\frac{5}{29}$$

Since \frac{33}{77} and \frac{42}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{33-42}{77}-\frac{8}{19}+\frac{5}{29}$$

Subtract 42 from 33 to get -9.

$$-\frac{9}{77}-\frac{8}{19}+\frac{5}{29}$$

Least common multiple of 77 and 19 is 1463. Convert -\frac{9}{77} and \frac{8}{19} to fractions with denominator 1463.

$$-\frac{171}{1463}-\frac{616}{1463}+\frac{5}{29}$$

Since -\frac{171}{1463} and \frac{616}{1463} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-171-616}{1463}+\frac{5}{29}$$

Subtract 616 from -171 to get -787.

$$-\frac{787}{1463}+\frac{5}{29}$$

Least common multiple of 1463 and 29 is 42427. Convert -\frac{787}{1463} and \frac{5}{29} to fractions with denominator 42427.

$$-\frac{22823}{42427}+\frac{7315}{42427}$$

Since -\frac{22823}{42427} and \frac{7315}{42427} have the same denominator, add them by adding their numerators.

$$\frac{-22823+7315}{42427}$$

Add -22823 and 7315 to get -15508.

$$-\frac{15508}{42427}$$

Factor

$$-\frac{15508}{42427} = -0.365521955358616$$